Question

How many liters of \[20%\] alcohol solution should be added to \[40\] liters of a \[50%\] alcohol solution to make a \[30%\] solution?

Answer 1

Hint : We know that a mixture is a combination of two or more two substances. We generally use ratio, percentage, or fractions to describe quantities in a mixture. The quantity of the alcohol that each part of the mixture adds to the final solution is equal to the quantity of each solution that is mixed.

Complete Step By Step Answer:
A mixture problem involves mixing two or more things and further determining quantities such as price, percentage, or concentration from that mixture. A system of equations can be used to solve mixture problems by developing equations to represent relations between known and unknown variables.
To determine how much water should be added to dilute a saline solution, or might want to know the percentage of concentrate in a jug of apple juice. Solving such types of mix slider or mixture problems generally involves solving systems of equations.
Let $x$ liters of \[20%~\] alcohol solution,
\[\Rightarrow 30%=\dfrac{\left[ x(20%)+40(50%) \right]}{x+40}\]
\[\Rightarrow \dfrac{30}{100}=\dfrac{\left[ x\left( \dfrac{20}{100} \right)+40\left( \dfrac{50}{100} \right) \right]}{x+40}\]
On further solving we get;
$\Rightarrow 20x+2000=30(x+40)$
Now by further simplifying to get the value of $x$ ;
$\Rightarrow 10x=800$
$\therefore x=80.$
Therefore the Required answer is \[80~\] liters.

Note :
Remember that the best approach to solve the mixture problem is to create a table that contains one row of each type of ‘item’ that has been mixed, and one column that contains every fact about the item. Once done, the table will have some blank space, corresponding to the information that is not given.